Solve for $t$, $ \dfrac{1}{5t^3} = -\dfrac{2}{t^3} - \dfrac{4t - 9}{2t^3} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $5t^3$ $t^3$ and $2t^3$ The common denominator is $10t^3$ To get $10t^3$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ \dfrac{1}{5t^3} \times \dfrac{2}{2} = \dfrac{2}{10t^3} $ To get $10t^3$ in the denominator of the second term, multiply it by $\frac{10}{10}$ $ -\dfrac{2}{t^3} \times \dfrac{10}{10} = -\dfrac{20}{10t^3} $ To get $10t^3$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{4t - 9}{2t^3} \times \dfrac{5}{5} = -\dfrac{20t - 45}{10t^3} $ This give us: $ \dfrac{2}{10t^3} = -\dfrac{20}{10t^3} - \dfrac{20t - 45}{10t^3} $ If we multiply both sides of the equation by $10t^3$ , we get: $ 2 = -20 - 20t + 45$ $ 2 = -20t + 25$ $ -23 = -20t $ $ t = \dfrac{23}{20}$